A timing belt drive between a servo motor and a ball screw. The belt slipped under acceleration. The customer had installed a 2:1 reduction but the belt was the wrong width. The motor was 750W, the screw needed 5 N·m at 3000 RPM. The belt was rated for 2 N·m. It slipped. This is how I size a timing belt drive.
The power and torque
Power from the motor: P = 750 W. The 2:1 reduction means the screw sees half the speed and double the torque. Screw speed = motor RPM / 2. Screw torque = motor torque × 2 × efficiency (0.95). Motor rated torque: T = P / ω = 750 / (3000 × 2π / 60) = 750 / 314 = 2.39 N·m. Screw torque = 2.39 × 2 × 0.95 = 4.54 N·m. During acceleration, the torque is 3x rated (for 0.2 s). Peak torque = 13.6 N·m. The belt must handle 13.6 N·m at the screw, or 6.8 N·m at the motor shaft (before the reduction).
The belt pitch and width
Timing belts are specified by pitch (MXL, XL, L, H) and width. The pitch determines the pulley tooth size. For a servo drive, I use H pitch (5 mm tooth) or L pitch (3 mm). The belt’s torque rating is in the catalog, per unit width. For an H-pitch belt, the rating is about 0.8 N·m per 10 mm width. For L-pitch, about 0.3 N·m per 10 mm width.
For our 6.8 N·m peak at the motor shaft: with H-pitch, I need width = 6.8 / 0.8 × 10 = 85 mm. That’s a wide belt. With L-pitch: 6.8 / 0.3 × 10 = 227 mm. Even wider. Something’s off — the customer had a 10 mm wide L-pitch belt. It was rated for 0.3 N·m. The peak torque was 6.8 N·m. It was 22x undersized. No wonder it slipped.
The correction factors
The catalog rating is for steady-state torque. For servo applications (frequent starts and stops, reversing), I multiply by a service factor of 2.5. The belt must handle the peak torque at 2.5x service factor. Required belt rating = 6.8 × 2.5 = 17 N·m. With H-pitch at 0.8 N·m per 10 mm: width = 17/0.8 × 10 = 212 mm. That’s huge.
Wait — that can’t be right. Let me reconsider. The catalog ratings for HTD timing belts are much higher. Let me use real numbers. An HTD 5M belt (5 mm pitch, 15 mm wide) is rated for about 8 N·m continuous, 20 N·m peak. That handles our 6.8 N·m peak with margin. The customer’s belt was an XL-pitch (not HTD) — an older, lower-capacity profile. The XL belt is fine for light conveyors, not servo axes.
What I specified
| Belt type | Pitch | Width | Rated torque (N·m) | Use for |
|---|---|---|---|---|
| MXL | 2.03 mm | 6 mm | 0.15 | Light (encoders, small actuators) |
| XL | 5.08 mm | 10 mm | 0.5 | Light (small motors, <100W) |
| L | 9.53 mm | 20 mm | 2.0 | Medium (100-400W) |
| HTD 3M | 3 mm | 15 mm | 3.0 | Small servo (100-400W) |
| HTD 5M | 5 mm | 15 mm | 8.0 | Standard servo (400-1000W) |
| HTD 8M | 8 mm | 20 mm | 25 | Large servo (1-3 kW) |
For our 750W servo, I specified an HTD 5M belt, 15 mm wide. Rated for 8 N·m continuous, 20 N·m peak. The peak requirement is 6.8 N·m. Margin is 3x. The belt doesn’t slip.
The pulley diameter effect
The belt’s torque rating is at the pulley. A smaller pulley means the belt tension is higher for the same torque (T = F × r). A 20 mm diameter pulley sees twice the belt tension of a 40 mm pulley. I use at least a 36-tooth HTD 5M pulley (114 mm diameter) for the motor. Smaller pulleys (20 tooth) put more stress on the belt and cause premature failure. The customer had a 20-tooth pulley — undersized.
The tensioning
A timing belt doesn’t need extreme tension — the teeth carry the torque. But too little tension causes tooth jumping (the belt rides over the pulley teeth). Too much tension overloads the bearings. The rule: tension the belt so you can deflect it 1/64 inch per inch of span with moderate finger pressure. For a 200 mm span, that’s about 3 mm deflection. I set the center distance so the belt has a slight preload — not tight, not loose. A spring-loaded tensioner takes up slack as the belt stretches.
The number I check: peak torque (motor rated × 2 for reduction × 3 for acceleration × 2.5 service factor), then select an HTD belt profile and width that exceeds it by 2x. Use a minimum 36-tooth pulley. Don’t use XL/L profile belts for servo axes — they’re for light conveyor duty. The belt that slipped was 20x too small for the torque.
